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Math Help - Integrals

  1. #1
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    Integrals

    find the following indefinite integral (using u substitution):

    \int x \sqrt[3]{x+1} dx


    evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):

    \int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx

    \int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}} dx
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  2. #2
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    Quote Originally Posted by qzno View Post
    find the following indefinite integral (using u substitution):

    \int x \sqrt[3]{x+1} dx


    evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):

    \int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx

    \int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}} dx
    1) Let u=x+1

    2) Let u=\tan x

    3) Let u=x^2+b^2
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  3. #3
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    I already tried this for them all haha
    Last edited by qzno; January 29th 2009 at 04:37 PM.
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  4. #4
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    for the second one I got the evaluated answer to be:

    \frac{(tan 1)^3}{3}

    is this correct?

    and i still cant do the last question : (
    thanks to anyone who helps!!
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  5. #5
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    For the first one when i let u = x + 1, i got the answer to be: \frac{3x(x+1)^{\frac{4}{3}}}{4} + c
    is this correct?

    i still havnt figured out the third one : (
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